We investigate an infinite dimensional partial differential equation of Isaacs' type, which arises from a zero-sum differential game between two masses. The evolution of the two masses is described by a controlled transport/continuity equation, where the control is given by the vector velocity field. Our study is set in the framework of the viscosity solutions theory in Hilbert spaces, and we prove the uniqueness of the value functions as solutions of the Isaacs equation.
A zero-sum differential game for two opponent masses / Bagagiolo, Fabio; Capuani, Rossana; Marzufero, Luciano. - In: SN PARTIAL DIFFERENTIAL EQUATIONS AND APPLICATIONS. - ISSN 2662-2963. - STAMPA. - 2025, 6:(2025), pp. 1901-1923. [10.1007/s42985-025-00322-5]
A zero-sum differential game for two opponent masses
Bagagiolo, Fabio;Capuani, Rossana;Marzufero, Luciano
2025-01-01
Abstract
We investigate an infinite dimensional partial differential equation of Isaacs' type, which arises from a zero-sum differential game between two masses. The evolution of the two masses is described by a controlled transport/continuity equation, where the control is given by the vector velocity field. Our study is set in the framework of the viscosity solutions theory in Hilbert spaces, and we prove the uniqueness of the value functions as solutions of the Isaacs equation.| File | Dimensione | Formato | |
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